9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
Which angle is an adjacent interior angle?
Triangle L M N. Angle L is 1, angle M is 2, angle N is 3. Side M N extends to form angle 4.
1
2
3
4
Step-by-step explanation:
Triangle LNM is an adjecent interior angle
Answer:
I think it's C
Step-by-step explanation:
Let me know if it's incorrect.
Write 2 1/4 as a decimal
Hey there!
2 1/4
= 2 * 4 + 1 / 4
= 8 + 1 / 4
= 9 / 4
= 9 ÷ 4
= 2.25
Therefore, your answer is: 2.25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The polynomial 3x² + mx? - nx - 10 has a factor of (x - 1). When divided by x + 2, the remainder is 36. What are
the values of m and n?
Answer:
[tex]m = 12[/tex]
[tex]n =3[/tex]
Step-by-step explanation:
Given
[tex]P(x) = x^3 + mx^2 - nx - 10[/tex]
Required
The values of m and n
For x - 1;
we have:
[tex]x - 1 = 0[/tex]
[tex]x=1[/tex]
So:
[tex]P(1) = (1)^3 + m*(1)^2 - n*(1) - 10[/tex]
[tex]P(1) = 1 + m*1 - n*1 - 10[/tex]
[tex]P(1) = 1 + m - n - 10[/tex]
Collect like terms
[tex]P(1) = m - n + 1 - 10[/tex]
[tex]P(1) = m - n -9[/tex]
Because x - 1 divides the polynomial, then P(1) = 0;
So, we have:
[tex]m - n -9 = 0[/tex]
Add 9 to both sides
[tex]m - n = 9[/tex] --- (1)
For x + 2;
we have:
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
So:
[tex]P(-2) = (-2)^3 + m*(-2)^2 - n*(-2) - 10[/tex]
[tex]P(-2) = -8 + 4m + 2n - 10[/tex]
Collect like terms
[tex]P(-2) = 4m + 2n - 10 - 8[/tex]
[tex]P(-2) = 4m + 2n - 18[/tex]
x + 2 leaves a remainder of 36, means that P(-2) = 36;
So, we have:
[tex]4m + 2n - 18 = 36[/tex]
Collect like terms
[tex]4m + 2n = 36+18[/tex]
[tex]4m + 2n = 54[/tex]
Divide through by 2
[tex]2m + n=27[/tex] --- (2)
Add (1) and (2)
[tex]m + 2m - n + n = 9 +27[/tex]
[tex]3m =36[/tex]
Divide by 3
[tex]m = 12[/tex]
Substitute [tex]m = 12[/tex] in (1)
[tex]m - n =9[/tex]
Make n the subject
[tex]n = m - 9[/tex]
[tex]n = 12 - 9[/tex]
[tex]n =3[/tex]
In a recent poll of 500 13-year-olds, many indicated to enjoy their relationships with their parents. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We wish to estimate the difference in proportions of 13-year old boys and girls who say that their parents are very involved in their lives. In the sample, 93 boys and 172 girls said that their parents are very involved in their lives. What is a 96% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?
(a) Calculate a 95% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?
(b) Interpret your interval calculated above.
Answer:
CI 96 % = ( - 0.1128 ; 0.0728 )
CI 95% = ( - 0.1087 ; 0.6878 )
The two intervals contain 0 value therefore we can support that there is not statistics difference between the two groups with confidence level of 96 % and 95%
Step-by-step explanation:
Boys sample:
sample size n₁ = 200
x₁ number of boys saying their parents are very involved in their lives
= 93
p₁ = x₁/n₁ = 93/200 = 0.465 then q₁ = 1 - p₁ q₁ = 1 - 0.465 q₁ = 0.535
Girls sample
sample size n₂ = 300
x₂ number of girls saying their parents are very involved in their lives
= 172
p₂ = x₂/n₂ = 172/ 300 = 0.573 then q₂ = 1 -0.573 q₂ = 0.427
CI 96 % α = 4 % α = 0.04 α/2 = 0.02
p₁ - p₂ = 0.465 - 0.573 = - 0.168
CI 96 % = ( p₁ - p₂ ) ± z(c) * SE
z(c) for α = 0.02 z(c) = - 2.05
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ ( 0.465*0.535)/200 + (0.573*0.427)/300
SE = √ 0.00124 + 0.000815
SE = √ 0.00205
SE = 0.0453
CI 96 % = ( -0.02 ± ( 2.05 * 0.0453 ) )
CI 96 % = ( -0.02 ± ( 0.0928 ))
CI 96 % = ( - 0.1128 ; 0.0728 )
a) CI 95% α = 5 % α = 0.05 α/2 = 0.025
SE = 0.0453
z(c) for 0.025 is from z-table z(c) = 1.96
CI 95% = ( - 0.02 ± 1.96 * 0.0453)
CI 95% = ( - 0.02 ± 0.08878 )
CI 95% = ( - 0.1087 ; 0.6878 )
The number of diners at a restaurant each day is recorded and a daily average is calculated every month (assume 30 days in a month). The number of diners each day has a mean of 107 and a standard deviation of 60, but does not necessarily follow a normal distribution.The probability that a daily average over a given month is greater than x is 2.5%. Calculate x. You may find standard normal table useful. Give your answer to 3 decimal places.x =
Answer:
x = 128.472
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The number of diners each day has a mean of 107 and a standard deviation of 60.
This means that [tex]\mu = 107, \sigma = 60[/tex]
Distribution of the daily average:
Over a month of 30 days, so [tex]n = 30, s = \frac{60}{\sqrt{30}} = 10.955[/tex]
The probability that a daily average over a given month is greater than x is 2.5%. Calculate x.
This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 107}{10.955}[/tex]
[tex]X - 107 = 1.96*10.955[/tex]
[tex]X = 128.472[/tex]
So x = 128.472
The club will use the majority criterion method to determine the final winner. However, while finalizing the votes, a member of the club discovers that Mason did not meet the original criteria to be considered for the vacation package, because he is a county deputy, not a city police person, so Mason is eliminated from the votes. Who actually will win the tickets? Is the irrelevant alternative criterion supported in this case?
Answer and Explanation:
The irrelevant alternative criterion states that if two candidates A and B contest for an election and candidate B is preferred to candidate A then any other candidate X should not cause candidate A to win the election.
In this case if Mason was candidate A, then candidate B should still win by the majority criterion method and the irrelevant alternative criterion would still be supported. However if he is candidate B then the irrelevant alternative criterion is not supported.
Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers salaries, companies mean, and standard deviation for each company
Brother Salary P sd
Tom 84000 75000 7000
Andy 70578 60000 8200
What is the 2-score of Andy's salary?
a. 1.89
b. 1.89
c. 1.29
d. 0-129
Answer:
c. 1.29
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Andy 70578 60000 8200
This means that [tex]X = 70578, \mu = 60000, \sigma = 8200[/tex]
What is the z-score of Andy's salary?
This is Z, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70578 - 60000}{8200}[/tex]
[tex]Z = 1.29[/tex]
So the correct answer is given by option c.
Solve (x + 3)2 + (x + 3) – 2 = 0.
9514 1404 393
Answer:
x = -5 or x = -2
Step-by-step explanation:
Factoring, we have ...
((x +3 +2)((x +3) -1)) = 0
(x +5)(x +2) = 0
x = -5 or x = -2 . . . . . . . . values that make the factors zero
Is the proportion 28/16 = 14/8 correct
Answer:
yes
Step-by-step explanation:
its correct because divide by 2/ 28/16=14/8
maybe
Please help me.I tryed to solve
Answer:
[tex]x \ge 1[/tex]
Step-by-step explanation:
Given
The number line
Required
Interpret
On the number, we have the following observations;
(1) The thick line starts from 1
(2) The line points to the right; this means greater than or/equals to
(3) The dot on 1 is a closed circle; this means greater than or equal to
So, the inequality is:
x greater than or equal to 1
i.e.
[tex]x \ge 1[/tex]
A ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 24t + 7. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Answer:
Step-by-step explanation:
Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.
If the position function is
[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is
v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:
0 = -32t + 24 and
-24 = -32t so
t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:
s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so
s(.75) = 16 feet
CHECK MY ANSWERS PLEASE
____
The sequence is geometric:
3, 13, 23, 33,...
True
False***
_____________________
The sequence is geometric:
5, -25, 125, -625,...
True***
False
Step-by-step explanation:
For a geometric sequence,
[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]
1. The sequence is :
3, 13, 23, 33,...
[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]
It is not geometric. It is false
2. The sequence is :
5, -25, 125, -625
[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]
So, the sequence is geometric as the common ratio is same. It is true.
PLEASE BE RIGHT AND SOLVE PLEASE
Answer:
That transformation that happened was B rotation since b is rotated 180 degrees from A
Hope This Helps!!!
Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $430 in interest, assuming she does not withdraw any of the money?
Answer:
The correct answer is - 7.166 years
Step-by-step explanation:
Given:
principle amount: 3000
rate of interest: 2%
time?
Interent to get: 430
Formula:
I = P*t*r/100
here p = principle
I = interest
r = rate of intrest and t = time
Solution putting value and deriving Time as formula:
(3000*2*t)/100 = 430
t = 43000/3000*2
= 7.166 years.
Find the value of x in each case:
If a woman makes $32,000 a year receives a cost of living increase 2.2% what will her new salary be?
Answer:
$32 704
Step-by-step explanation:
(102.2÷100) × 32 000 = $32 704
Use the expression 9(7 + 2x) to answer the following:
Part A: Describe the two factors in this expression. (4 points)
Part B: How many terms are in each factor of this expression? (4 points)
Part C: What is the coefficient of the variable term? (2 points)
Step-by-step explanation:
Part A:
The two factors in 9(7+2x) are 9 and 7+2x
Part B:
First term: 9
Second term: 7+2x
Part C:
9(7+2x)
Open bracket
63+18x
The coefficient is 18x
A. The two factors are 9 and (7+2x).
B. In first factor, only one term and in second factor , two terms i.e. 7 and 2x are present.
C. The coefficient of the variable term is 18.
Algebraic expression:Given expression is;
[tex]9(7+2x)[/tex]
In given expression, there are two factors fist is 9 and second one is [tex](7+2x)[/tex]
In first factor, only one term and in second factor , two terms i.e. 7 and 2x are present.
To find the coefficient of variable term, we have to to expand given expression.
[tex]9(7+2x)=63+18x[/tex]
The coefficient of the variable term is 18.
Learn more about the algebraic expression:
https://brainly.com/question/4344214
help i’ll give brainliest please hurry
How is solving for speed similar to solving for time?
O They both require that two numbers be added.
O They both require that two numbers be subtracted
O They both involve writing a rate.
O They both use the same units of measure.
Answer:
third one
Step-by-step explanation:
Type the correct answer in each box.
Jessica has $24 and plans to spend it all at the grocery store. She wants to purchase bags of carrots and bagels. Bags of
carrots cost $2 each, and bagels cost $3 per bag. Let x represent the number of bags of carrots and y represent the
number of bags of bagels. Complete the equation in standard form that models this scenario.
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y=(
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Step-by-step explanation:
Jessica has $24 and plans to spend it all at the grocery store.Bags of carrots cost $2 each, and bagels cost $3 per bag.Let x represent the number of bags of carrots and y represent the number of bags of bagels.the cost for the 'x' bags of carrots = $2xand the cost for the 'y' bags of bagels = $3ySo, the equation would be,so the equation in standard form that models the given scenario is
2x + 3y = 24
2x + 3y = 24ab=6cm ac=12 calculate the length of cd
Answer:
is that the full question?
Answer:
Solution:-
Given,
ab =perpendicular (p)= 6cm
ac =hypotenuse (h)= 12cm
cd =base (b)= ?
using , Pythagoras theorem we have ,
b²=√h²-p²
or,cd²=√ac²-ab²
= √12²-6²
= √144-36
=√108
=√10.8²
=10.8cm
the length of cd is 10.8 cm
hope it is helpful to you
Sam thinks of a 4 digit number. The digit in the one’s place is 3 less than the digit in the ten’s place and digit in thousand’s place is 5 less than the digit in hundred’s place. The value of the hundred’s place is 800. The digit in ten’s place is the greatest even number. What is the number Sam is thinking of?
9514 1404 393
Answer:
3885
Step-by-step explanation:
The hundreds digit is 8, and the thousands digit is 5 less, so is 3.
The tens digit is 8 (the largest even digit), and the ones digit is 3 less, so is 5.
The number is ...
3885
one particular ice cream parlor has 28 different flavors available. How many ice cream cups are possible if you order 4 scoops? this is a combination
Answer:
20,475 cream cups are possible.
Step-by-step explanation:
The order in which the flavors are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
4 cups from a set of 28.
So
[tex]C_{28,4} = \frac{28!}{4!24!} = 20475[/tex]
20,475 cream cups are possible.
Cell Phone Service
Cellular phone service is available for $31 per month for 666 minutes. What is the
monthly cost per minute? Round your answer to the nearest tenth of a cent.
The cost for the phone service is
cents per minute.
9514 1404 393
Answer:
4.7¢/min
Step-by-step explanation:
To find the cost in cents per minute, divide the cost in cents by the number of minutes.
$31.00/(666 min) = (3100¢)/(666 min) ≈ 4.7¢/min
Some number times 7 is equal to the number increased by 9
Answer:
.
Step-by-step explanation:
.
The scale of a map is 1/8 inch=10 miles. If two cities are 3 inches apart on the map how many miles are they from each other
Given the function
Calculate the following values:
f( - 1) =
f(0)
f(2)=
-1 is less than 0, so you use the first equation:
3(-1) +2 = -3+2 = -1
f(-1) = -1
For 0 use the 2nd equation:
3(0) + 4 = 0+4 = 4
f(0) = 4
For 2 use the 2nd equation:
3(2) + 4 = 6+4 = 10
f(2) = 10
SOMEONE HELP ASAP PLES NO EXPLANATOIN NEEDED PLS LEAVE UR ANSWER AS TEXT (SOME TIMES I CAN'T SEE IMAGES) THANK YOU SO MUCH!!!
Answer:
i cant see the image
Step-by-step explanation:
ayúdenme por favor, es de matemática.
Answer:welcome to brainly
Step-by-step explanation:
Hello there! My name is agenthammerx, a Master Answerer and Engagement Team Member here on Brainly. I am here to welcome you to the site! Thank you for taking initiative to check out Brainly and for posting your first question! The Brainly Community welcomes you. If you have any questions regarding anything about the site, please don’t hesitate to reach out to me! I will try my best to help you and answer your question or check out our help center at https://faq.brainly.com/
What's more to do? Task 1 Directions: Solve for the volume of the following: A. Rectangular Prism 1.1-9 m w 4 m h = 3 m 2.1 = 10 cm w=7 cm h = 15 cm 3.1 = 14 m w= 10 m h=9 m B. Cube 4. s = 12 cm 5. s= 6m
Answer:
Step-by-step explanation:
A). Volume of a rectangular prism = Length × Width × Height
= lwh
1). Volume of a rectangular prism if the measures of the sides are,
Length (l) = 9 cm
Width (w) = 4 cm
Height (h) = 3 cm
Therefore, volume = lwh
= 9 × 4 × 3
= 108 cm³
2). Length = 10 cm
Width = 7 cm
Height = 15 cm
Volume = lwh
= 10 × 7 × 15
= 1050 cm³
3). Length = 14 cm
Width = 10 cm
Height = 9 cm
Volume = 14 × 10 × 9
= 1260 cm³
B. Volume of a cube = (Side)³
4). If the measure of one side = 12 cm
Volume of the cube = (12)³
= 1728 cm³
5). If the measure of one side = 6 cm
Volume of the cube = (6)³
= 216 cm³
